Research

With Yongmiao Hong

Abstract: This paper proposes the range-based estimator to avoid long-run variance estimation in hypothesis testing about the population mean of a time series process. The denominator of the range-based estimator is the so-called adjusted range normalizer which makes use of the well-established properties for adjusted range analysis in measuring long range dependence. Compared to current hypothesis testing approach, the range-based estimator can get rid of choosing tuning parameter or kernel function. In the meantime, the range-based estimator has salient property in the way that it takes into account of the extreme value property in time series data especially under heavy tail distributions. The concrete probability density function form and critical values for the asymptotic distribution for the range-based estimator can be derived explicitly. We perform asymptotic local power comparisons for the range-based estimator and related tests which shows that the range-based estimator has remarkable asymptotic local power performance against a broad class of asymptotic local alternatives. Simulation results reveal incorporating MBB can generally improve the size performance of the range-based estimator in testing the process where the size performance of the range-based estimator is deviate much from the true significance level. Real data analysis for S & P 500 percentage returns series and macroeconomic series also indicates  the range-based estimator has outstanding power performance especially when data depicts larger volatility and more observations are available.